Ambient spaces of dimensional dual arcs
type: Item
instance of: scholarly article
title: Ambient spaces of dimensional dual arcs
zbMATH Open document ID: 1086.51009
DOI: 10.1023/B:JACO.0000022564.51008.63
published in: Journal of Algebraic Combinatorics
publication date: 2004-08-06T00:00:00Z
review text: Generalizing the family of 1-dimensional subspaces namely of the tangents of an arc a \(d\)-dimensional dual arc in a finite projective space \(PG(n,q)\) is defined. Those of maximal cardinality are called dual hyperovals and those dual arcs which are not part of a bigger one are called complete dual arcs. The author is only interested in the case \(d>1\). He asks for an upper bound on \(n\) given \(d\) and \(q\). It is shown that for dual hyperovals and a lot of smaller subsets in the case \(q\neq 2\) one has \(n\geq d(d+3)/2=:D\) and that this bound is best possible. In the last part the author constructs \(d\)-dimensional dual arcs in connection with quadric Veroneseans in \(PG(D,q)\).
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51A45
zbMATH DE Number: 2081995
zbMATH Keywords: dual arc
zbMATH Keywords: dual hyperoval
zbMATH Keywords: Veronesean
author: Satoshi Yoshiara
reviewed by: Herbert Hotje
MaRDI profile type: Publication
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full work available at URL: b:jaco.0000022564.51008.63
OpenAlex ID: W2042744965
description: scientific article; zbMATH DE number 2081995